Having the wrong length spokes by itself wont cause the wheel to have any problems. If the spoke is to short, you might not have enought thread engagement for the nipple/spoke interface to grab. If the spoke is to long, it will either bottom out on the spoke, which will ensure you never have proper spoke tension, or the top of the spoke will punch a hole in your tube.
If the spokes are breaking they are fatigued. If you are breaking more than 2, then they are all fatigued, the ones that have broken, more so than the ones that have not, but they will all eventuall break.
So, you definately need new spokes. Do you need a new rim? Once all the spokes have been removed, does it resemble a taco? if so, then yes. If it is still true, and there is no cracking around the eyelets or where the spokes join the rim, then it should be good to go, however check for brake track wear.
Bikes shops dont like building with second hand stuff becuase you cant always tell from a visual inspection what is fatigued and its better for the bike shop to start fresh, that way there should be no problems.
Not enough tension will fatigue the spokes and they will break. Too much tension and you will crack and/or deform rims.
I have a bike that gets ridden about 11,000km a year. I go through a bit of stuff, especially rear rims. I have not replaced the rear spokes in the last 6 years, but have gone through 3 rims. The spokes are not fatiguing because they are held at correct tension.